Theorem 2.3 ([1]})
If \(({\cal E},{\cal F})\)  is irreducible recurrent,
then for any nearly Borel non-exceptional set \(B\) ,
\(P_x(\sigma _B\circ \theta _n<\infty \ \text{for any $n\ge 0$})=1, \quad \text{q.e.\ $x\in X$}.\) 

